>Rationality Tables:
Applying Polarizing Nonmaterial Monads in Risk Analysis

>by Dallas F. Bell, Jr.

1. Introduction

Rationality can be explained as behavior derived from the perception of what's best based on chosen compliance with or noncompliance with nonmaterial realities. Those perceptions are obtained from the logic of the chosen authority which sets the standard of good and bad--deity. Study of the infinite deity, God, is commonly known as systematic theology and contains the foundational corpus of all nonmaterial realities called monads. The corpus of monads is used to calibrate the logic system of both believers and nonbelievers in God. Decision options are not infinite and must be either compliant with or noncompliant with reality, or truth. An example of a decision from the material monad of gravity results in only two possible outcomes of either acting on compliance with the truth of gravity or noncompliance with the truth of gravity, "no" gravity. Likewise, if the nonmaterial monad of love is not complied with the only other option, "no" love, must be acted on.

The monads in systematic theology, an infinite discipline, are relational and dependant sets and subsets of all options of rationality. (Please see the paper by Dallas F. Bell, Jr. titled The Monads of Systematic Theology: Forming a Nonexhaustive Treebank and Logical Operators for Decision Theory.) Analysts of the logic systems of individuals and/or the groups they ultimately form should have an epistemological understanding of rational possibilities. The probability of their respective behavior(s) can then be predicted with greater accuracy. For example, risk analysts assess information regarding levels of risk for individuals and societies. Their estimation and evaluation processes would be incomplete without the input of relevant behavioral/rationality categories concerning the subject of their analysis.

Human polarizing goals to comply with or not comply with material or nonmaterial monads are key to understanding specific rationalities for behavior(s) including those associated with risk. This paper will use the tool of rationality tables to address the nonmaterial monads that encompass the cause and effect of all rationalities.

2. Rationality Tables

Rationality tables are constructed from the entities, or monads, of systematic theology. Each self-existent monad is relational and dependant. They form strings which create dyads and triads sets of bivalent logic. The monads are positioned in sets to reflect the highest stratified monad(s) from left to right. They are represented by (1) if the polarizing goal of the subject is determined to be compliance with the monad to be analyzed. The polarizing goal of noncompliance is represented by (0). Two monads of (1,1) would equal a set of truth, represented by the logic symbol T, because they are compliant with reality. Two monads of (0,0) may equal a set of false, represented by the logic symbol F, because they are not compliant with reality or be considered truly consistent logic which is represented by T. Two monads of (1,0) or (0,1) would also equal sets that are false, F, because they are not completely compliant with reality.

"No" means x is dependent and can't exist to any degree. "Not" means x may partially exist as defined but the existence is in an incomplete state. It is prudent to primarily use "no" since "not" implies incorrect and untrue logic as demonstrated by the dyad subsets of a monad x of (1,0) or (0,1) that equal false, F.

The rationality tables employ the Boolean style operators of the conjunction "and" and the condition of if and only if, "iff". A dyad table would have the following possibilities of a logic set (x,y).

"and"
(0,0) = F, but is consistent logic of the lowest order of compliance with realities
(0,1) = F, inconsistent logic of a low induction order of compliance with realities
(1,0) = F, inconsistent logic of a higher deduction order of compliance with realities
(1,1) = T, consistent logic of the highest order of compliance with realities

"iff" biconditional
(0,0) = T, though it's not compliant with realities it is consistent logic
(0,1) = F, because it is inconsistent logic
(1,0) = F, because it is inconsistent logic
(1,1) = T, because it is consistent logic

A triad table of a logic set (x,y,z) is structured as follows.

"and"
(0,0,0) = F, lowest
(0,0,1) = F
(0,1,0) = F
(1,0,0) = F
(0,1,1) = F
(1,0,1) = F
(1,1,0) = F
(1,1,1) = T, highest

"iff" triconditional
(0,0,0) = T, doesn't comply with realities but is consistent logic
(0,0,1) = F
(0,1,0) = F
(1,0,0) = F
(0,1,1) = F
(1,0,1) = F
(1,1,0) = F
(1,1,1) = T

Dyad and triad tables that reflect the classifications and symbols (T equals theology and leads to the respective tracks of R, B, W, and E) in systematic political science are:

dyad of a logic set (x,y)
(1,1) = T1, the highest level of compliance with realities
(1,0) = T2
(0,1) = T3
(0,0) = (long term is an overall unsurvivable level of noncompliance with realities)

triad of a logic set (x,y,z)
(1,1,1) = T1, the highest level of compliance with realities
(1,1,0) = +T2
(1,0,1) = T2
(0,1,1) = - T2
(1,0,0) = +T3
(0,1,0) = T3
(0,0,1) = - T3
(0,0,0) = (long term is an overall unsurvivable level of noncompliance with realities)

The above rationality tables function to extend the expected utility of probability analysis further into the realm often defined as bounded rationality. Obviously, rationality by finite minds is cognitively limited or bound by finite knowledge and capabilities. The monad of faith in the present logic system of a subject should be expected to be applied by the subject during times of uncertainty and the subject's logic momentum of direction followed, unless the circumstances force the subject to accept reality in order to survive.

3. Risk Analysis

Risk is the human expression of the degree of probability of expectation of perceived loss. The term risk implies the freewill to choose within the finite knowledge of possibilities. The rationality of each person's logic system can be analyzed using the rationality tables. For example, if there is a need to determine the fire insurance payment scales for home owners in a region it would be vital to know what the percentage of past fire damages were attributable to arson by the policy holders. A dyad for arson could be created from the monads of stealing, or "no" Lb8, and bearing false witness, or "no" Lb9 producing the (0,0) set of logic. People that are accessed with the set (0,0) should be considered as having a high risk for arson behavior, the sets of (0,1) and (1,0) should be considered as moderate risks, and a set of (1,1) should be considered a low risk to attempt to profit from arson. Any test to determine those logic sets can expect the subject with a (1,1) logic set to express their true beliefs. However, subjects with (1,0) and (0,1) sets may change their responses to reflect a position they perceive will contribute to their receiving a more favorable policy than if they expressed their true beliefs. Subjects with a (0,0) set will likely conceal their beliefs and may even attempt to reflect a (1,1) logic set. It is important to use as many monads as is possible to create dyads and triads that point to the logic that is attempting to be determined for predicting a behavior.

If the leaders of two nation-states were to conduct talks to iron out differences they too can be analyzed. If both leaders and their nation-states have equal (1,1) logic sets of relevant monads such as love and justice an outcome with low risk of failure can be expected. If they have (1,0) or (0,1) logic sets a higher risk of failure should be the expected outcome and if they each have a (0,0) logic set failure should likely result. On the other hand, if each leader and their nation-states have unequal logic the one with the (1,1) set of logic should be expected to be cautious of the other that has either a (1,0) or (0,1) set of logic and should not be expected to trust the one with a (0,0) logic set. If one has either a (1,0) or (0,1) logic set they may be expected to trust the one with a (1,1) or (1,0) or (0,1) set of logic but not be expected to trust the one with a (0,0) logic set. If one has a (0,0) logic set they should not be expected to trust those with either a (0,1) or (1,0) or (1,1) logic set.

Risk analysts may use rationality tables to improve other analytical tools such as fuzzy analysis which is used to determine the relative behavior of individuals in a group or region. META game theory formulae provide a platform to plot behavior and find behavioral momentum. Rev. Thomas Bayes' theorem is often used to merge old data with the latest information to find the most recent probability. Bayes' theorem is an equation where the probability of A occurring, given the occurrence of B, is proportional of all occurrences of B in which A also occurs. The computational version is that A and B are random events that are probability related. The probability of A occurs, given the occurrence of B, is given in the quotient. The numerator is the probability of B occurring, given the occurrence of A, multiplied by the probability of A occurring. The denominator states the same term again but has added the probability of B occurring, given the nonoccurrence of A multiplied by the probability of A not occurring. Bayes' theorem aids in modeling sensitivity, the accuracy of modeling uncertainly by averaging referred to as Bayes' model averaging.

4. Conclusion

Hopefully, it has been demonstrated that the rationality tables are an essential tool for analysts and especially risk analysts for predicting probable individual and group behavior. The paper has also indirectly indicated the value of using the systematic political science category of T1 compliance with realities. The short list of ultimate realities, or monads, in systematic theology is considered by many people to be God, Jesus, salvation, and eternal existence. The T1 triads with a polarizing consistent logic set of (1,1,1) would reflect the true sets of (God, Jesus, salvation) and (Jesus, salvation, heaven). The T3 triads of polarizing consistent logic set of (0,0,0) would reflect the untrue sets of (no God, no Jesus, no salvation) and (no Jesus, no salvation, no heaven). To know these realities and reject them evokes the monad of reprobation, or hardening the heart toward future compliance with realities. Meaning that to reject nonmaterial realities produces eternal material consequences. Axiomatically, it takes less faith and less risk to comply with realities than to reject them.

In conclusion, math and logic are mere mechanisms that reflect their input which may or may not be accurate regarding probabilities. The human subjects of an analysis should be considered as always having the freewill to change direction at any time. Analysts that remain cognizant of that reality and other truths should have enhanced sensitivity levels and experience greater overall success than those that choose to ignore the monads of systematic theology.

--ALL RIGHTS RESERVED (2005) Dallas F. Bell, Jr.--